{
 "metadata": {
  "name": "arsenic_wells_switching"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from pandas import *\n",
      "from statsmodels.formula.api import logit\n",
      "from statsmodels.nonparametric import KDE\n",
      "import matplotlib.pyplot as plt\n",
      "from patsy import dmatrix, dmatrices"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Logistic models of well switching in Bangladesh\n",
      "\n",
      "Our data are information on about 3,000 respondent households in Bangladesh with wells having an unsafe amount of arsenic. The data record the amount of arsenic in the respondent's well, the distance to the nearest safe well (in meters), whether that respondent \"switched\" wells by using a neighbor's safe well instead of their own, as well as the respondent's years of education and a dummy variable indicating whether they belong to a community association.\n",
      "\n",
      "Our goal is to model well-switching decision. Since it's a binary variable (1 = switch, 0 = no switch), we'll use logistic regression.\n",
      "\n",
      "This analysis follows Gelman and Hill *Data Analysis Using Regression and Multilevel/Hierarchical Models*, chapter 5.4. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = read_csv('data/wells.dat', sep = ' ', header = 0, index_col = 0)\n",
      "print df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   switch  arsenic       dist  assoc  educ\n",
        "1       1     2.36  16.826000      0     0\n",
        "2       1     0.71  47.321999      0     0\n",
        "3       0     2.07  20.966999      0    10\n",
        "4       1     1.15  21.486000      0    12\n",
        "5       1     1.10  40.874001      1    14\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model 1: Distance to a safe well\n",
      "\n",
      "For our first pass, we'll just use the distance to the nearest safe well. Since the distance is recorded in meters, and the effect of one meter is likely to be very small, we can get nicer model coefficients if we scale it. Instead of creating a new scaled variable, we'll just do it in the formula description using the `I()` function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model1 = logit('switch ~ I(dist/100.)', df = df).fit()\n",
      "print model1.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 2038.118913\n",
        "         Iterations 4\n",
        "                           Logit Regression Results                           \n",
        "==============================================================================\n",
        "Dep. Variable:                 switch   No. Observations:                 3020\n",
        "Model:                          Logit   Df Residuals:                     3018\n",
        "Method:                           MLE   Df Model:                            1\n",
        "Date:                Sat, 22 Dec 2012   Pseudo R-squ.:                 0.01017\n",
        "Time:                        13:05:25   Log-Likelihood:                -2038.1\n",
        "converged:                       True   LL-Null:                       -2059.0\n",
        "                                        LLR p-value:                 9.798e-11\n",
        "==================================================================================\n",
        "                     coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "----------------------------------------------------------------------------------\n",
        "Intercept          0.6060      0.060     10.047      0.000         0.488     0.724\n",
        "I(dist / 100.)    -0.6219      0.097     -6.383      0.000        -0.813    -0.431\n",
        "==================================================================================\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot this model. We'll want to jitter the `switch` data, since it's all 0/1 and will over-plot. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def binary_jitter(x, jitter_amount = .05):\n",
      "    '''\n",
      "    Add jitter to a 0/1 vector of data for plotting.\n",
      "    '''\n",
      "    jitters = np.random.rand(*x.shape) * jitter_amount\n",
      "    x_jittered = x + np.where(x == 1, -1, 1) * jitters\n",
      "    return x_jittered"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dist_logit_par = model1.params['I(dist / 100.)']\n",
      "plt.plot(df['dist'], binary_jitter(df['switch'], .1), '.', alpha = .1)\n",
      "plt.plot(np.sort(df['dist']), model1.predict()[np.argsort(df['dist'])], lw = 2)\n",
      "plt.ylabel('Switched Wells')\n",
      "plt.xlabel('Distance from safe well (meters)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x109862990>"
       ]
      },
      {
       "output_type": "display_data",
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QSCRUxzg/P0+5XCYcDpPJZBgcHCQUCuH1ejl58iTFYlElbLWOzmQy4fV66evr47777lPT\nEBaLhUwmo1YLNRoNtYyxXq+Tz+cJBALYbDa2b99OpVIhnU6zc+fOs879ax37ysoKZrMZvV5PoVDA\narWqEcLp0x7JZJJkMkksFiOdTtPT06NyINp3rk1HRKNRotGoqjHQ3qtNn2kBRuvwV1ZW1nSo2hx3\nLBajUqlgMpmIxWJYrdbzzntv9pyytuxXp9NdFXPw4upxoYHgoi0f/aC0lSRGo5FIJILL5cLlcqll\ne52dnbhcLk6dOkVXV5danthoNHA4HKpeQLta1ul0NDU1YTAYaGlpIZPJqI6vXq+rEUi9XlfTTtqU\nkTZ/XiqVVPIxGo1SLBax2Wyk02m2bdtGLpejWq1iMBiIx+Ps3r2ber3Oo48+SlNTE6+//jq33nor\n+XxetVWv19Pe3s7y8rJaGeR0OjGZTBw9epRoNIrJZGJqagqz2axqAJLJJE6nk2QySb1ex+Vy0dPT\nQ61Wo7W1lZdeeomBgQGOHTvG3NwcJpMJk8nEyMiISrJHo1GMRiOhUIjp6WluuukmNTLy+Xzs2LFj\nze/k9FyA9hn9fj9LS0vAahDQRlSxWAyXy8XS0hJ6vV5Nu1UqFYxGI8lkkmKxSCQSwe/3v29FSCaT\nIZvNsrCwQHt7O7VajWAwqH6X51pZZDQaiUajGAwGlpaWMBqNG75yRqvb+CCrnIS4Ulx2IwJYTXjE\n43Gy2SwtLS3UajXVYZfLZWw2G3v27CESibCwsECtVsNsNqsKUm3+PpvNqqSkXq9XlaEGg4FKpUIm\nk1FLTGG1MlcrSNIqfb1eL+FwmFKpRLlcxmQyYTAYVKc4NDTEyZMn1RTL9u3bGRoaUsnimZkZFaCa\nm5ux2+243W5MJpNKTGtFcx0dHSwsLNDc3KzqEwqFgko21+t1Vc0ci8Xo6elRbb7mmmvwer1UKhXq\n9TqJRILFxUWKxSLZbJZ4PK5GCLlcjomJCdLptEp2t7W1AbBr1673JXLtdjvz8/O0tLSQSCTU49oI\nIJvNEggEMJvNKnGsrezRrp61q/STJ0+STqeJxWI0Gg3sdjsmk0mNUIxGoyoILJVKtLW10dTUpFYZ\naaOJmZkZlpeXVft0Oh2pVAqr1aqm4LQ6B21565lGIB/Wh5keEuJiuepGBJFIhDfffJO3336bVCpF\nJpNhaWmJarWK2WympaWF1tZWstks5XJZXfFp9QIA7e3tpFIp7HY7VqsVl8ulrua1pHGlUlFLTLUO\nQ5ua6urqIhwO43a78fv9TE9PUyqVMBqNaruK66+/HqfTSbFYpLOzk0gkQldXF11dXSwtLbF7925y\nuRz9/f2USiWampro7e1leXmZpqYm6vU6IyMjaqpFK9wC1EhDWzm1fft26vU6119/PbA6baKtjHK7\n3fT29tLZ2alW9GhFVG63m9nZWaxWq9oWQ+uotakarT179uxZs+LgvSuIBgcH1WocrQCsUCgQi8Vw\nu91qGqe1tVUV5en1ejVaGBwcVEEhkUhQKpXI5/Ps3buXUCgErK540eoRzGYzbW1t6PV6fD7fms62\nWCxSKpWo1+uEw2GMRiM+n0+NJjKZjMolaFft51qT/mHW3mv5ldPrIoaGhiQYiCvaZTciyOfzzMzM\nMDMzw+LiIhMTE7S0tBAKhVQFrc1mI5lMqo5Zm0bR5um1lUPa8tBGo6G2adC2QTCbzRgMBgwGA1ar\nlaamJux2O319fUQiEfbu3UtPTw9er5eWlha6u7vVSiOr1UpzczM9PT1YrVaSySSNRoP29naVz3C7\n3XR1damtH7R6A7vdTjQaZdeuXZhMJlZWVlQVdDabVZ8znU5jNBrZsWMHuVyO++67TwWrarXKyMgI\n5XIZj8dDJBIhFArR1dWF0WhUQVD7DrSpqpGREaanp1WOo1gs0traqoKOduU8MzPDxMQEgLrKNxgM\n5HI5DAaDSshrgVebOuvr68PhcKgcjLb/ifbdNxoNbDabmhZqb2+nWq0CqyuQstks3d3dFItFVYR3\npivvlZUVNR1nNpvVa04fTUSjUfx+vxoFnSt/8N6198Vi8Zyjh5WVlTV1EetdBSXERrnqksWZTIaF\nhQUikQgrKytkMhk1ndDe3k6lUlnT8Wnz+9qmc4VCgXK5TC6Xo1wuq7Xv2iqefD6vVuNoxUZalXC5\nXKbRaNDc3KyWjt5xxx04nU5OnDhBLBZDp9NRr9epVqvce++9LCwsYDKZWF5eJpPJEIlEqNfrZLNZ\n0uk06XSaxcVF1Sklk0lqtRrpdBqfz0dLSwt2u52Wlhbi8TiVSoWJiQkMBoOqPB4cHGRgYIDJyUni\n8bjah6inp4exsTG1D5J2patVHOdyOXVFfMMNN2AwGNT5tc/e39+vViMlk0neeustZmZmVMAxm830\n9vaSSqWw2Wyq0+3r61PTdalUak1hmrZqRet8taW32vFO3xMpGAyqJY8Oh4NYLEa1WqW5uRmj0bgm\nAQ2rf+jaCi6tOE0baWhTiblcjq6uLmq1murYy+UymUyGvr6+9019vTdIvHcZ7Xs7ebvdTjqdXvMZ\nZEQgLqWrLhBUq1V27txJKBTC6XQyNjaGXq9X/6VSKcxmM06nk1KpxJ49e5ibmyOXy5HL5dTKDq0K\nuNFoqI5xZWVFLfc0m804HA6q1Srlcpl8Po/T6USv16vEcm9vL/V6nRdeeIETJ06odfM2m41AIMD4\n+DiTk5Nq1VK1WiUajVIul2ltbVW7hSYSCSqViqp90KYy5ufnKRaLZDIZlTOYn59XU1XxeFztjVSr\n1VhYWMBisZBKpdRy1HA4rLZwcLlcKjns8XgwGo24XC7a29uJxWKUSiUmJibUaqt9+/apZKxWWzE5\nOUk4HKZQKNDe3q62utA6S71eT19fn5oiiUajOBwOEomECm5ap3h6B69NR7W2tqqgoJ1XCx7a8bR8\ni/a9nB5ItPoG7T9tKWsqlaLRaLC4uKh+19oKKC25e7Zlpe9de3++1Ufvrav4sEFgo/IVQmiuukBg\ntVrVzo5jY2Ok02kSiQRms1nN3+r1eoxGI7feeiu1Wk11GvV6nZaWFur1OgaDQU3FaMP31tZWjMbV\ntIjdbqfRaKiVJtrKHZvNhtfrpampic7OTk6dOsXo6KiqSi4UCjidTlZWVohGo6oTikQiajO1zs5O\nGo0GoVCIU6dOYTAYcDqdagrG7/erefFQKMTQ0JDaGkKrTHa73bjdblwul5q6KJfLjI2NEQgEiEQi\nHDlyhJmZGebn52lqalLTMhaLhWq1SiAQWDONMzs7y7Fjx9QGdsViUU15JZNJNdrQ6XR0dnayd+9e\ntaOq1lmentjV/ui0xL621YcWsLV1/+/dRuJsa92TySTpdFpt4dDf30+1Wl0TSN7b8WrtMpvNKnDo\n9Xqy2awaFWiPn6tjP709H6Qo60LW619N20CIy8NVFwhgddXQG2+8QSQSwWazEY/HVSKzqakJnU7H\nTTfdRDqdplwuU6vV1L4y2tSDtr/Pjh07VJ2AyWTCbrerq2UtqaxdRWurZxwOB4ODg5hMJqanpxkf\nH1cdnJaUzWQyKmegrdrR1s/v3LkTg8GA3W4nk8mQz+dV5XBbWxtzc3N0dHSQyWQwGAxqKeu2bdso\nFosEAgF6e3sxmUy8/fbbaiTjdDrVfRZmZmbUVFetVlPV1k6nk0AgQDgcJh6Pq3oEbepKm1Yql8vs\n27dPjQS071/bFHDnzp20tbWRTCbVCh2bzaY2iNM6Mb/fTzqdVh282+1Wu7meqUL5dO8tHtM2GdRW\n5QQCAXXlf7aOWeuQC4WCyhtoBW1a8Ojr6zvn1fuZrtA3syhL9tARG+2qCwTanhlvvfUWx44dY35+\nnmAwqCqKOzs71U6bk5OTLC4uqjXwHo+HTCZDtVpV+/mUy2W8Xi9OpxOz2UwikVBXjVp+IZ/P09TU\npO6DoNfryeVyhEIhIpGImmPWitS0TufWW29lZmZG3ZzG7/dz7bXXqoK4aDSq5uIrlYqqhNbr9UxP\nT6PX62lpacFoNNLX18evf/1r3G43FouFzs5OtWx1YGBA3c9Bmz5LJBL09vaSSCTUNNTu3buxWCyE\nQiF1LwStTsFms7G0tMTg4CCVSoVPfepTpNNp1dFrQWDv3r1rOnatUC8ejxMKhchms2oKTevEfD6f\neo+2ZFcrVDtXR/fe4rFarUYkEsHtduPxeNQ0zgfpmE/PG7S2tq4ZhZxrq4nT23GxrtDfG9hkqkhc\nqKsuEOTzeXK5HM8884wqChoZGSGXyzE7O8vy8jILCwtks1m1rFTrvFdWVtQduGw2GxaLhdtvv13d\nQaxQKKg7mGnJQ21dvLYdtcvlwuFwYLPZmJ2dJZvNquWfRqNR7eLZ0dGhdv7UVh1pW1Y7nU5uuOEG\nRkdHVS5Au8PYNddcw/z8vKpstlgs7N27l4WFBbX1tslkUsfMZrMA3HLLLXR3d5NIJGhqamLv3r0U\nCgXuueceNZ2lrfDJZrMYjUa18Zs2OrnvvvsoFovs27ePdDrNqVOn1LbdpVIJl8ul7umgrcLSrs61\nz6Btg93S0qJW82h7PJ04cQKv14vb7aZYLNLX16emnc7UyWlXxqVSCbfbTblcplQqqY0A37vNxbk6\nSy1noT33QYKHdsx4PP6BAtdGeW/bZKpIXKirLhBoV/S5XI5EIqGmGPr6+nj99deB1V0gtflnvV6P\ny+VSV9yNRoNAIKDW2udyOYrFokpmzs/Ps7KyoipktSDS1dWlKmqj0SjpdBqz2czAwIBahgqrla/a\n/HVfXx8Wi4VwOKzuadDR0UE+n1fFYtqSS51Ox/bt29V6dW3vo76+PnXlr+VDdDqdul+B2Wzm2muv\n5ZZbblE319HufnbXXXepkY5Op8PhcGA2m7FarapYzu/3Ew6H6ejowGAw0N3djV6vZ2ZmhkgkopKs\n/f39OBwOPB6PSv4CatO4RqOBy+WiVqupqR6t4wqFQiwuLlIoFFQeYXh4eM2005mWZmoJ4N7eXrWi\nyOv1qtHd6X/Um9FZasc8fSXUB5062kgyVSQu1FUXCKrVqtp6oKmpifb2dj7ykY+QTqfVFs2VSoW2\ntjZ8Ph89PT1quZ+2f49WYaoNu7V7AWhTQdrUkLbVQ1NTE01NTTQ3N2Oz2dT8srZvvs/nU2vUg8Gg\n2i3U7/cTi8XUHb+cTiepVIrl5WU6OztVVXIqlVKB6oYbbsDv9zM1NaU+y/DwMIuLi6pD1+7c5vf7\n8Xg8apSjFc3lcjmGh4dVBa1WIawleg0Gg8oxaKuZWltbMZvNqjOemJhQnVtfX5+aUtGuqrXlkdoK\nKm2KqKenB6fTuabj0rbYbjQaajSkLdE819LMarWqVhlp8/zaPkrv3d1zMzrL01dCtbS0rEmCn6vO\nYKOv2K+mHUPFpXHVBQKr1UogEMDpdKq18lriU6/XE4vFGB4eVleopxeQuVwucrkc6XRaXfFryw8B\n1VFpt8PUAkJXV5dKQrtcLkKhEL29vfT19WG32xkaGiIUCpFIJHA6nfT09LB//34ikYg6ZldXl0p8\nplIpksmk2mbaZrORz+dVAVWj0aBQKBAMBjEajSQSCQYGBtQS0M7OTgYGBtS9mrdv304mk6FYLFIs\nFnG73UQiEXVfXi3vof3n9XpV0Vy5XKanpwePx6OmPrTOOBwOEwgE6OjoULkMWLs80mQyMTs7i06n\nU/coNhqNxGIxHA6HWlUE4HK51HJTzZmWZmrbUmjbX2sBu1wuq60sisXimg55MzrL0495rtqBi7GZ\nnewYKi7EVRcIANVB6PV67HY72WyWYrHInj171B479Xodo9Gopl60m564XC51Ny9t6wav10sgEKCn\npwe9Xs8999yjbtXocDgIBAJqKsdisbBr1y48Hg933323+mKLxaK6v+/OnTvV/vtaTcLtt9+uAhBA\nMBhUWxZot8689tprcTgcaj5fK6a6/vrr1b48fr+fYDDI7t27sVqttLa2qjt8tbS00NTUhM1mU1M0\ntVqNnp4etdrI5XKpwi+dTsfAwIBahnl6Z6yNDrRbiL63g9M6J+0qWfucfX19asR1+sohk8l0xmKt\nMy3NPL1WQOt0tR1KtU739H2CznScjXCm4rdzLVGVK3Zxubrq7lAG795lR7vbUjweV6t3tCmIRCKh\nto7Qto2wtpDBAAAgAElEQVSwWq10dHQwOzurCrm0moL29nZWVlbUCiJtOWixWCQej3PTTTfxzDPP\ncPfdd9PZ2UmhUGDHjh2EQiFeeeUV1flWq1V6enoIBAKUy2VOnjzJ4OCg2pXypz/9KU6nU+0zpE3t\neDwe6vU6jUZDVfuurKywY8cOotEoS0tL6kbu7e3t6g5c2l2aKpUK4XAYr9erpnxSqRS7du1Cp9Op\nOzlpIwWd7ux3qNKO6fF4znoHL42Wv0gmk+zevRu9Xn/Bd8E60/tP/11ro5eLeYctuRuWuJJd6B3K\nLutAcHqHFYvFSCQSbNu2jampKVVopd3sXrsjWTwep9FoqPcCeDwe9Rrthu3btm0jHo+rTd20wKJN\ni2idgXYct9vN5OQkHo9H7dX/3o5D2/dIa7O2ekXb4Oxsna92+8MznV9zekd1pnOf6XUb0aGd6XgX\neo5zHfODBCchxFpXdSAQQghxfhfad374O4gLIYS4qkggEEKILU4CgRBCbHESCIQQYouTQCCEEFuc\nBAIhhNjiJBAIIcQWJ4FACCG2OAkEQgixxUkgEEKILU4CgRBCbHESCIQQYouTQCCEEFucBAIhhNji\nJBAIIcQWJ4FACCG2OONGH/DQoUOk02kikQhf+cpXGBwcVM/99Kc/5ec//zl+v59KpcL3vvc9uQuV\nEEJcYhsaCJ577jlee+01Hn74YcbGxvjc5z7HCy+8oJ7/gz/4A8bGxvB4PDz00EM888wz3HPPPRvZ\nBCGEEB/Shk4NHT58mFtvvRWAoaEhjh8/TjabVc93dHTw/e9/n2KxSCaTYWhoaCNPL4QQYh02NBAk\nEgkcDof62eFwqHtpAvzpn/4pzz//PL29vYyMjBAMBjfy9EIIIdZhQwNBIBAgl8upn3O5nOrs5+bm\n+NGPfsTTTz/N+Pg4Y2NjfOc739nI0wshhFiHDQ0EDz74IC+//DIAY2NjjIyMMDs7y+LiIuVymVKp\nBIDL5eK2224jn89v5OmFEEKsw4Ymi2+55Rauu+46/uiP/ohQKMSPf/xjDh06xN69e/niF7/Ib/zG\nb/C5z30Ou91OMpnkBz/4wUaeXgghxDroGo1G41I3QqPlEwKBwCVuiRBCXDkutO+UgjIhhNjiJBAI\nIcQWJ4FACCG2OAkEQgixxUkgEEKILU4CgRBCbHESCIQQYouTQCCEEFucBAIhhNjiJBAIIcQWJ4FA\nCCG2OAkEQgixxUkgEEKILU4CgRBCbHESCIQQYouTQCCEEFucBAIhhNjiJBAIIcQWJ4FACCG2OAkE\nQgixxUkgEEKILU4CgRBCbHESCIQQYouTQCCEEFucBAIhhNjiJBAIIcQWJ4FACCG2OAkEQgixxV12\ngeCN+RSpQuVSN0MIIbYM46VuwHv9xeExqs8tcmOPm/t2Brhzux+nxXSpmyWEEFctw9e+9rWvnesF\nv/mbv0lPTw+HDx/mYx/7GNVqlX379m1KY/L5POOhLMsrMJcs8IupGP/wq3mOL2eoNRq0t1gxGy+7\nQYwQQlxS+XweALvdvq73n3dEsHPnToaHh/mt3/ot3n77bf7rf/2v6zrRB/XnDw5jdrh4djLKkyci\nvD6X5MWZOC/OxDEZxrmlz8t9OwPcvs2H3XzZDWiEEOKKc96edGpqittuu43/8B/+A9lslomJiU1v\nlMtm5lN7O/jU3g4S+fJqUBgP88Z8iuenYjw/FcNs0HNbv5f7BgPs6/dhNRs2vV1CCHE10jUajca5\nXlAqlRgfH2fv3r0cPXqUZDLJHXfcsSmNiUQiAAQCgTM+H8uXeHZiNSj8eiGN1vAmo57bB3zcuzPA\nbf1eLCYJCkKIreN8fef5nDUQ/Pf//t/XvlCno9Fo8PTTT/P3f//36zrZ+XyYDxPJlnh6IsJT4xHe\nXkqrx60mA7cPeLl3Z5Bb+z00GSUoCCGubpsWCB566CGuu+66NY81Gg1effVVHn300XWd7HzW+2FC\nmSJPn4jw1IkIx5Yz6nG72cDt23zctzPILX0eTAZJNAshrj6bFggikcgZD7q8vExbW9u6TnY+F/ph\nAJbSBZ4+EeHJ8Qhj4ax63GkxcveOAPcPBflIpwuDXnfB7RVCiMvBpgWCgwcPcqanXn31VR555JGz\nHvDQoUOk02kikQhf+cpXGBwcXPP8D37wA375y1+yd+9evvjFL655biMCwekWUis8NR7h8HiYqWhe\nPe6zm7lvMMj9Q0GGW5vR6SQoCCGuXBfad5511dCpU6e48847aTQaqqNsNBpMTU2d9WDPPfccr732\nGg8//DBjY2N87nOf44UXXlDPf+tb3yKbzfI//sf/WFdjP6xOl43P3NzLZ27uZTqW44mxMIfHIiym\nC/yv1+f5X6/P0+mycv9QkI8OBun3rW8NrhBCXMnOOiJYWVnBZrMBsLS0RDqdZufOnSwtLdHZ2XnG\ng/3Jn/wJLS0tfPnLXwbA4/EwOztLc3Mz+Xyenp4ePvvZzzI9Pc3AwAB/+Zd/idH4biza6BHBmTQa\nDY4vZzg8HubJ8QjxfFk9t93v4KNDQT46GKC9xbppbRBCiI10oX3nWbOnWhD4sz/7Mw4cOMDXv/51\n9Ho9f/VXf3XWgyUSCRwOh/rZ4XCoBo6OjuJ2u/na177GT3/6U0ZHR/nxj3+8rkZfCJ1Ox672Fv6/\nu3fwyO/dxg9+8xo+uaed5iYjk9Ecf/X8NL/xo5f5nf/5Ov/0xsKaQCGEEFej8xaUrays8NZbb/Hd\n734XWB0dnE0gECCXy6mfc7kcwWAQgKamJsxmswowd999N6OjoxfU+Atl0Ou4ocfDDT0evnjPDo6c\ninN4LMzz0zHeXkrz9lKabz0zwQ3dHu4fDrJ/ux9Hk1QzCyGuLuft1aLRKG+//Tb1ep3jx4+zvLx8\n1tc++OCDfOMb3wBgbGyMkZERZmdncblcbN++nWQySTqdpqWlhfHxce6+++6N+yQXyGzUc8c2P3ds\n87NSrvLCdJzDYyFePpngldnV/77xxAlu6/fy0aEg+6RwTQhxlThvZfHx48f53Oc+x9GjRxkcHORv\n/uZvuOaaa876+oMHDxKPxwmFQhw8eJBDhw6pFUL/8i//wt///d/T3d2NXq/nm9/85pr3XowcwYeV\nLlR4ZiLCE+Or+x5pX5bNZOCu7X4eGA5yQ48bo15qFIQQl8amLR999dVXufHGG9ffsnW4HAPB6aK5\nEk+NR3h8LMRo6N0aBa/NzH1DAQ4MtzIUlOWoQoiLa9MCwe7du7n99tu5/vrrueOOO9i2bdv6W/kB\nXe6B4HTzyRUOj4V5bDTMXHJFPd7ttnFgOMgDw0E6XbZL2EIhxFaxaYHgySef5M477+S1117jpZde\nYnJyklqtxp49e/jjP/7j9bf4HK6kQKBpNBqMhrI8PhbiybEI8ZV3VxntbndyYLiVe3cGcNvMl7CV\nQoir2aYVlN13330AWCwWisUib731FtlsFrfbva4TXa10Oh0jbU5G2pz80V3beG02yeOjYZ6djHJ0\nKcPRpQzfemaSW3o9PDDcyp3bfJJkFkJcVs46Ivjd3/1dnnrqKbZt28bHPvYxPv7xj7N9+/ZNbcyV\nOCI4m0K5xvPTMR4bDXHkZIL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tVa+DXW0t7BtYDQyScL58SSAQQmyYueQKL03HeXEmxhvz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\nBRRQwHcc/w9eY+u9Rb3DYgAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another way to look at this is to plot the densities of distance for switchers and non-switchers. We expect the distribution of switchers to have more mass over short distances and the distribution of non-switchers to have more mass over long distances."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kde_sw = KDE(df['dist'][df['switch'] == 1])\n",
      "kde_nosw = KDE(df['dist'][df['switch'] == 0])\n",
      "\n",
      "kde_sw.fit()\n",
      "kde_nosw.fit()\n",
      "\n",
      "plt.plot(kde_sw.support, kde_sw.density, label = 'Switch')\n",
      "plt.plot(kde_nosw.support, kde_nosw.density, color = 'red', label = 'No Switch')\n",
      "plt.xlabel('Distance (meters)')\n",
      "plt.legend(loc = 'best')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.legend.Legend at 0x109da8b50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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pJy5fvmz7GoQQ1YaEjZ0ymUw0dHOD9HTbPdB5sxudBBo0aICPjw+7d++2fQ1C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\n/vvf/xIdHc17771Hz549K74/UaPl5+d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      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model 2: Distance to a safe well and the arsenic level of own well\n",
      "\n",
      "Next, let's add the arsenic level as a regressor. We'd expect respondents with higher arsenic levels to be more motivated to switch."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model2 = logit('switch ~ I(dist / 100.) + arsenic', df = df).fit()\n",
      "print model2.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 1965.334134\n",
        "         Iterations 5\n",
        "                           Logit Regression Results                           \n",
        "==============================================================================\n",
        "Dep. Variable:                 switch   No. Observations:                 3020\n",
        "Model:                          Logit   Df Residuals:                     3017\n",
        "Method:                           MLE   Df Model:                            2\n",
        "Date:                Sat, 22 Dec 2012   Pseudo R-squ.:                 0.04551\n",
        "Time:                        13:05:29   Log-Likelihood:                -1965.3\n",
        "converged:                       True   LL-Null:                       -2059.0\n",
        "                                        LLR p-value:                 1.995e-41\n",
        "==================================================================================\n",
        "                     coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "----------------------------------------------------------------------------------\n",
        "Intercept          0.0027      0.079      0.035      0.972        -0.153     0.158\n",
        "I(dist / 100.)    -0.8966      0.104     -8.593      0.000        -1.101    -0.692\n",
        "arsenic            0.4608      0.041     11.134      0.000         0.380     0.542\n",
        "==================================================================================\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Which is what we see. The coefficients are what we'd expect: the farther to a safe well, the less likely a respondent is to switch, but the higher the arsenic level in their own well, the more likely."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Marginal effects\n",
      "\n",
      "To see the effect of these on the probability of switching, let's calculate the marginal effects at the mean of the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model2.margeff(at = 'mean')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "array([-0.21806505,  0.11206108])"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, for the mean respondent, an increase of 100 meters to the nearest safe well is associated with a 22% lower probability of switching. But an increase of 1 in the arsenic level is associated with an 11% higher probability of switching."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Class separability\n",
      "\n",
      "To get a sense of how well this model might classify switchers and non-switchers, we can plot each class of respondent in (distance-arsenic)-space. \n",
      "\n",
      "We don't see very clean separation, so we'd expect the model to have a fairly high error rate. But we do notice that the short-distance/high-arsenic region of the graph is mostly comprised switchers, and the long-distance/low-arsenic region is mostly comprised of non-switchers."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "logit_pars = model2.params\n",
      "intercept = -logit_pars[0] / logit_pars[2]\n",
      "slope = -logit_pars[1] / logit_pars[2]\n",
      "\n",
      "dist_sw = df['dist'][df['switch'] == 1]\n",
      "dist_nosw = df['dist'][df['switch'] == 0]\n",
      "arsenic_sw = df['arsenic'][df['switch'] == 1]\n",
      "arsenic_nosw = df['arsenic'][df['switch'] == 0]\n",
      "plt.figure(figsize = (12, 8))\n",
      "plt.plot(dist_sw, arsenic_sw, '.', mec = 'purple', mfc = 'None', \n",
      "         label = 'Switch')\n",
      "plt.plot(dist_nosw, arsenic_nosw, '.', mec = 'orange', mfc = 'None', \n",
      "         label = 'No switch')\n",
      "plt.plot(np.arange(0, 350, 1), intercept + slope * np.arange(0, 350, 1) / 100.,\n",
      "         '-k', label = 'Separating line')\n",
      "plt.ylim(0, 10)\n",
      "plt.xlabel('Distance to safe well (meters)')\n",
      "plt.ylabel('Arsenic level')\n",
      "plt.legend(loc = 'best')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.legend.Legend at 0x109f7cb10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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5Ut9//7127twpSfrrr790yy23qFixYurUqZOqV6+e01/RuHFjzZ07Vxs3blRKSsp148x+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\nZDB20VzniP9oJZ4+BVSl1KKIfQb19/9m78ZFlJzU4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iMFqYG4qrLxmjQG4chlll34xlOQ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\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model 3: Adding an interation\n",
      "\n",
      "It's sensible that distance and arsenic would interact in the model. In other words, the effect of an 100 meters on your decision to switch would be affected by how much arsenic is in your well. \n",
      "\n",
      "Again, we don't have to pre-compute an explicit interaction variable. We can just specify an interaction in the formula description using the `:` operator."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model3 = logit('switch ~ I(dist / 100.) + arsenic + I(dist / 100.):arsenic', \n",
      "                   df = df).fit()\n",
      "print model3.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 1963.814202\n",
        "         Iterations 5\n",
        "                           Logit Regression Results                           \n",
        "==============================================================================\n",
        "Dep. Variable:                 switch   No. Observations:                 3020\n",
        "Model:                          Logit   Df Residuals:                     3016\n",
        "Method:                           MLE   Df Model:                            3\n",
        "Date:                Sat, 22 Dec 2012   Pseudo R-squ.:                 0.04625\n",
        "Time:                        13:05:33   Log-Likelihood:                -1963.8\n",
        "converged:                       True   LL-Null:                       -2059.0\n",
        "                                        LLR p-value:                 4.830e-41\n",
        "==========================================================================================\n",
        "                             coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------------------\n",
        "Intercept                 -0.1479      0.118     -1.258      0.208        -0.378     0.083\n",
        "I(dist / 100.)            -0.5772      0.209     -2.759      0.006        -0.987    -0.167\n",
        "arsenic                    0.5560      0.069      8.021      0.000         0.420     0.692\n",
        "I(dist / 100.):arsenic    -0.1789      0.102     -1.748      0.080        -0.379     0.022\n",
        "==========================================================================================\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The coefficient on the interaction is negative and significant. While we can't directly intepret its quantitative effect on switching, the qualitative interpretation gels with our intuition. Distance has a negative effect on switching, but this negative effect is reduced when arsenic levels are high. Alternatively, the arsenic level have a positive effect on switching, but this positive effect is reduced as distance to the nearest safe well increases."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model 4: Adding educuation, more interactions and centering variables\n",
      "\n",
      "Respondents with more eduction might have a better understanding of the harmful effects of arsenic and therefore may be more likely to switch. Education is in years, so we'll scale it for more sensible coefficients. We'll also include interactions amongst all the regressors.\n",
      "\n",
      "We're also going to center the variables, to help with interpretation of the coefficients. Once more, we can just do this in the formula, without pre-computing centered variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model_form = ('switch ~ center(I(dist / 100.)) + center(arsenic) + ' +\n",
      "              'center(I(educ / 4.)) + ' +\n",
      "              'center(I(dist / 100.)) : center(arsenic) + ' + \n",
      "              'center(I(dist / 100.)) : center(I(educ / 4.)) + ' + \n",
      "              'center(arsenic) : center(I(educ / 4.))'\n",
      "             )\n",
      "model4 = logit(model_form, df = df).fit()\n",
      "print model4.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 1945.871775\n",
        "         Iterations 5\n",
        "                           Logit Regression Results                           \n",
        "==============================================================================\n",
        "Dep. Variable:                 switch   No. Observations:                 3020\n",
        "Model:                          Logit   Df Residuals:                     3013\n",
        "Method:                           MLE   Df Model:                            6\n",
        "Date:                Sat, 22 Dec 2012   Pseudo R-squ.:                 0.05497\n",
        "Time:                        13:05:35   Log-Likelihood:                -1945.9\n",
        "converged:                       True   LL-Null:                       -2059.0\n",
        "                                        LLR p-value:                 4.588e-46\n",
        "===============================================================================================================\n",
        "                                                  coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "---------------------------------------------------------------------------------------------------------------\n",
        "Intercept                                       0.3563      0.040      8.844      0.000         0.277     0.435\n",
        "center(I(dist / 100.))                         -0.9029      0.107     -8.414      0.000        -1.113    -0.693\n",
        "center(arsenic)                                 0.4950      0.043     11.497      0.000         0.411     0.579\n",
        "center(I(educ / 4.))                            0.1850      0.039      4.720      0.000         0.108     0.262\n",
        "center(I(dist / 100.)):center(arsenic)         -0.1177      0.104     -1.137      0.256        -0.321     0.085\n",
        "center(I(dist / 100.)):center(I(educ / 4.))     0.3227      0.107      3.026      0.002         0.114     0.532\n",
        "center(arsenic):center(I(educ / 4.))            0.0722      0.044      1.647      0.100        -0.014     0.158\n",
        "===============================================================================================================\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Model assessment: Binned Residual plots\n",
      "\n",
      "Plotting residuals to regressors can alert us to issues like nonlinearity or heteroskedasticity. Plotting raw residuals in a binary model isn't usually informative, so we do some smoothing. Here, we'll averaging the residuals within bins of the regressor. (A lowess or moving average might also work.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def bin_residuals(resid, var, bins):\n",
      "    '''\n",
      "    Compute average residuals within bins of a variable.\n",
      "    \n",
      "    Returns a dataframe indexed by the bins, with the bin midpoint,\n",
      "    the residual average within the bin, and the confidence interval \n",
      "    bounds.\n",
      "    '''\n",
      "    resid_df = DataFrame({'var': var, 'resid': resid})\n",
      "    resid_df['bins'] = qcut(var, bins)\n",
      "    bin_group = resid_df.groupby('bins')\n",
      "    bin_df = bin_group['var', 'resid'].mean()\n",
      "    bin_df['count'] = bin_group['resid'].count()\n",
      "    bin_df['lower_ci'] = -2 * (bin_group['resid'].std() / \n",
      "                               np.sqrt(bin_group['resid'].count()))\n",
      "    bin_df['upper_ci'] =  2 * (bin_group['resid'].std() / \n",
      "                               np.sqrt(bin_df['count']))\n",
      "    bin_df = bin_df.sort('var')\n",
      "    return(bin_df)\n",
      "\n",
      "def plot_binned_residuals(bin_df):\n",
      "    '''\n",
      "    Plotted binned residual averages and confidence intervals.\n",
      "    '''\n",
      "    plt.plot(bin_df['var'], bin_df['resid'], '.')\n",
      "    plt.plot(bin_df['var'], bin_df['lower_ci'], '-r')\n",
      "    plt.plot(bin_df['var'], bin_df['upper_ci'], '-r')\n",
      "    plt.axhline(0, color = 'gray', lw = .5)\n",
      "    \n",
      "arsenic_resids = bin_residuals(model4.resid, df['arsenic'], 40)\n",
      "dist_resids = bin_residuals(model4.resid, df['dist'], 40)\n",
      "plt.figure(figsize = (12, 5))\n",
      "plt.subplot(121)\n",
      "plt.ylabel('Residual (bin avg.)')\n",
      "plt.xlabel('Arsenic (bin avg.)')\n",
      "plot_binned_residuals(arsenic_resids)\n",
      "plt.subplot(122)\n",
      "plot_binned_residuals(dist_resids)\n",
      "plt.ylabel('Residual (bin avg.)')\n",
      "plt.xlabel('Distance (bin avg.)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.text.Text at 0x10ae3ef50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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9589L8I6PlxNeqYnAwEAYjca6r41GI4KCgho95oEHHsADDzyAO++8E6tWrcJDfC+JiBi2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\niy44zejHH4GJE4GFC6XyDEhAvOkm6bv85BMJe35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      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model 5: log-scaling arsenic\n",
      "\n",
      "The binned residual plot indicates some nonlinearity in the arsenic variable. Note how the model over-estimated for low arsenic and underestimates for high arsenic. This suggests a log transformation or something similar.\n",
      "\n",
      "We can again do this transformation right in the formula."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model_form = ('switch ~ center(I(dist / 100.)) + center(np.log(arsenic)) + ' +\n",
      "              'center(I(educ / 4.)) + ' +\n",
      "              'center(I(dist / 100.)) : center(np.log(arsenic)) + ' + \n",
      "              'center(I(dist / 100.)) : center(I(educ / 4.)) + ' + \n",
      "              'center(np.log(arsenic)) : center(I(educ / 4.))'\n",
      "             )\n",
      "\n",
      "model5 = logit(model_form, df = df).fit()\n",
      "print model5.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 1931.554102\n",
        "         Iterations 5\n",
        "                           Logit Regression Results                           \n",
        "==============================================================================\n",
        "Dep. Variable:                 switch   No. Observations:                 3020\n",
        "Model:                          Logit   Df Residuals:                     3013\n",
        "Method:                           MLE   Df Model:                            6\n",
        "Date:                Sat, 22 Dec 2012   Pseudo R-squ.:                 0.06192\n",
        "Time:                        13:05:57   Log-Likelihood:                -1931.6\n",
        "converged:                       True   LL-Null:                       -2059.0\n",
        "                                        LLR p-value:                 3.517e-52\n",
        "==================================================================================================================\n",
        "                                                     coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------------------------------------------\n",
        "Intercept                                          0.3452      0.040      8.528      0.000         0.266     0.425\n",
        "center(I(dist / 100.))                            -0.9796      0.111     -8.809      0.000        -1.197    -0.762\n",
        "center(np.log(arsenic))                            0.9036      0.070     12.999      0.000         0.767     1.040\n",
        "center(I(educ / 4.))                               0.1785      0.039      4.577      0.000         0.102     0.255\n",
        "center(I(dist / 100.)):center(np.log(arsenic))    -0.1567      0.185     -0.846      0.397        -0.520     0.206\n",
        "center(I(dist / 100.)):center(I(educ / 4.))        0.3384      0.108      3.141      0.002         0.127     0.550\n",
        "center(np.log(arsenic)):center(I(educ / 4.))       0.0601      0.070      0.855      0.393        -0.078     0.198\n",
        "==================================================================================================================\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And the binned residual plot for arsenic now looks better."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arsenic_resids = bin_residuals(model5.resid, df['arsenic'], 40)\n",
      "dist_resids = bin_residuals(model5.resid, df['dist'], 40)\n",
      "plt.figure(figsize = (12, 5))\n",
      "plt.subplot(121)\n",
      "plot_binned_residuals(arsenic_resids)\n",
      "plt.ylabel('Residual (bin avg.)')\n",
      "plt.xlabel('Arsenic (bin avg.)')\n",
      "plt.subplot(122)\n",
      "plot_binned_residuals(dist_resids)\n",
      "plt.ylabel('Residual (bin avg.)')\n",
      "plt.xlabel('Distance (bin avg.)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.text.Text at 0x10aebb590>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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f3Gci8g4N7b80KSMhIiIiIvIFDLaJiIhcyGAwICYmBnq9Hvn5+Vo3h4hUxmCb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\nxhhjjDGmJNxsM8YYY4wxpiT/B3B5eyHROWJVAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Model error rates\n",
      "\n",
      "The `pred_table()` gives us a confusion matrix for the model. We can use this to compute the error rate of the model.\n",
      "\n",
      "We should compare this to the null error rates, which comes from a model that just classifies everything as whatever the most prevalent response is. Here 58% of the respondents were switchers, so the null model just classifies everyone as a switcher, and therefore has an error rate of 42%."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print model5.pred_table()\n",
      "print 'Model Error rate: {0: 3.0%}'.format(\n",
      "    1 - np.diag(model5.pred_table()).sum() / model5.pred_table().sum())\n",
      "print 'Null Error Rate: {0: 3.0%}'.format(\n",
      "    1 - df['switch'].mean())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[  568.   715.]\n",
        " [  387.  1350.]]\n",
        "Model Error rate:  36%\n",
        "Null Error Rate:  42%\n"
       ]
      }
     ],
     "prompt_number": 18
    }
   ],
   "metadata": {}
  }
 ]
}